相关论文: Using the Navier-Cauchy equation for motion estima…

Thanks to its capability of acquiring full-view frames at multiple kilohertz, ultrafast ultrasound imaging unlocked the analysis of rapidly changing physical phenomena in the human body, with pioneering applications such as ultrasensitive…

In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate…

In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…

The reconstruction task in photoacoustic tomography can vary a lot depending on measured targets, geometry, and especially the quantity we want to recover. Specifically, as the signal is generated due to the coupling of light and sound by…

We establish the time decay rates of the solution to the Cauchy problem for the compressible Navier-Stokes-Poisson system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of…

Measuring the dynamics and mechanical properties of muscles and joints is important to understand the (patho)physiology of muscles. However, acquiring dynamic time-resolved MRI data is challenging. We have previously developed…

Ultrasound modulation of electrical or optical properties of materials offers the possibility to devise hybrid imaging techniques that combine the high electrical or optical contrast observed in many settings of interest with the high…

In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…

We prove space-time decay estimates of suitable weak solutions to the Navier-Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result…

A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…

Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers.…

The main respiratory muscle, the diaphragm, is an example of a thin structure. We aim to perform detailed numerical simulations of the muscle mechanics based on individual patient data. This requires a representation of the diaphragm…

In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned problem by replacing integer derivatives with fractional…

Estimating the shape and motion state of the myocardium is essential in diagnosing cardiovascular diseases.However, cine magnetic resonance (CMR) imaging is dominated by 2D slices, whose large slice spacing challenges inter-slice shape…

The same type of objects in different images may vary in their shapes because of rigid and non-rigid shape deformations, occluding foreground as well as cluttered background. The problem concerned in this work is the shape extraction in…

We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…

In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…

This paper is concerned with the global smooth non-vacuum solutions with large data to the Cauchy problem of the one-dimensional compressible Navier-Stokes equations with degenerate temperature dependent transport coefficients which satisfy…

This paper aims at mathematically modeling a new multi-physics conductivity imaging system incorporating mechanical vibrations simultaneously applied to an imaging object together with current injections. We perturb the internal…